The cylindrical bottle sells for $54.00, the conical bottle sells for $20.00 and the spherical bottle for $35. What is the best buy per cubic centimeter of perfume? Why?
To determine the best buy per cubic centimeter of perfume, we need to calculate the volume of each bottle and divide the price by the volume.
Cylindrical bottle:
The price is $54.00 and the bottle is cylindrical, so its volume can be calculated using the formula for the volume of a cylinder: V = π * r^2 * h, where r is the radius and h is the height.
Assuming the radius of the bottle is r = 5 cm and the height is h = 10 cm, the volume would be:
V = π * (5 cm)^2 * 10 cm ≈ 785.4 cm^3
The price per cubic centimeter would be:
$54.00 / 785.4 cm^3 ≈ $0.07/cm^3
Conical bottle:
The price is $20.00 and the bottle is conical, so its volume can be calculated using the formula for the volume of a cone: V = (1/3) * π * r^2 * h, where r is the radius and h is the height.
Assuming the radius of the cone is r = 4 cm and the height is h = 8 cm, the volume would be:
V = (1/3) * π * (4 cm)^2 * 8 cm ≈ 134.04 cm^3
The price per cubic centimeter would be:
$20.00 / 134.04 cm^3 ≈ $0.15/cm^3
Spherical bottle:
The price is $35.00 and the bottle is spherical, so its volume can be calculated using the formula for the volume of a sphere: V = (4/3) * π * r^3, where r is the radius.
Assuming the radius of the sphere is r = 3 cm, the volume would be:
V = (4/3) * π * (3 cm)^3 ≈ 113.04 cm^3
The price per cubic centimeter would be:
$35.00 / 113.04 cm^3 ≈ $0.31/cm^3
Comparing the prices per cubic centimeter, we can see that the cylindrical bottle is the best buy with $0.07/cm^3. It has the lowest price per unit volume among the three options.